Equilibrium electrode potentials electrical double layer

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

In the closely related coulostatic method based on injection of a charge from a small condenser into an electrode in equilibrium with a redox system. The resulting time dependence of the electrode potential originates from the discharging of the electrical double layer by electrode reactions... 

E is the standard equilibrium potential, i. e. the potential corresponding to unit activity and RTF. The dissolution reaction leads to the development of an electrical double layer at the iron-solution interface. The potential difference of the Fe/Fe " half cell cannot be measured directly, but if the iron electrode is coupled with a reference electrode (usually the standard hydrogen electrode, SHE), a relative potential difference, E, can be measured. This potential is termed the single potential of the Fe/Fe electrode on the scale of the standard hydrogen couple H2/H, the standard potential of which is taken as zero. The value of the equilibrium potential of an electrochemical cell depends upon the concentrations of the species involved. 

When two conducting phases come into contact with each other, a redistribution of charge occurs as a result of any electron energy level difference between the phases. If the two phases are metals, electrons flow from one metal to the other until the electron levels equilibrate. When an electrode, i.e., electronic conductor, is immersed in an electrolyte, i.e., ionic conductor, an electrical double layer forms at the electrode-solution interface resulting from the unequal tendency for distribution of electrical charges in the two phases. Because overall electrical neutrality must be maintained, this separation of charge between the electrode and solution gives rise to a potential difference between the two phases, equal to that needed to ensure equilibrium. 

Activation Processes. To be useful in battery applications reactions in list occur at a reasonable rate The rare or ability of battery electrodes to produce current is determined by the kinetic processes of electrode operations, not by thermodynamics, which describes the characteristics of reactions at equilibrium when the forward and reverse reaction rates are equal. Electrochemical reaction kinetics follow the same general considerations as those of bulk chemical reactions. Two differences are a potential drop that exists between the electrode and the solution because of the electrical double layer at the electrode interface, and the reaction that occurs at a two-dimensional interfaces rather than in three-dimensional space. 

When a metal is immersed in a solution of an electrolyte, a potential difference is set up at the ra tal—solution interface this is the electrode potential. When a metal dips into a solution of its own ions, some ions may leave the metal and enter the solution, while others will deposit on the metal from solution. Since the ions are charged, an electrical double layer is created at the metal—solution interface. The equilibrium potential difference between metal and solution is the Galvani potential. When ions are transferred from solution to deposit on the metal, the metal consititutes the positive side of the double layer and vice versa. 

In the previous section the mercury electrode has been described. If no redox pairs (e.g. Fe2+ and Fe3+) are in solution and if we exclude gas reactions, the mercury electrode is completely polarizable. Polarizable means If a potential is applied, a current flows only until the electric double layer has formed. No electrons are transferred from mercury to molecules in the solution and vice versa. The other extreme is a completely reversible electrode, for which the Agl electrode is an example. Each attempt to change the potential of an Agl electrode leads to a current because the equilibrium potential is fixed by the concentrations of Ag+ or I according to the Nernst equation. 

The electrostatic aspects of electrochemical systems will be introduced first and the electrochemical potential as a key concept is presented (Sects. 1.2-1.4). The electrochemical equilibrium is discussed and Nemst s equation and standard and formal electrode potentials are introduced (Sect. 1.5). The study of electrochemical interfaces under equilibrium ends with the phenomenological and theoretical treatment of the electrical double layer (Sect. 1.6). 

As discussed above, concentration gradients will produce a potential drop. Because of the electrode reaction even at equilibrium, that is, with no current flow, there will be a potential drop. The formation of this metal-electrolyte potential difference, which is based on a metal-ion potential, arises from the transfer of metal ions from the metal into the electrolyte, and vice versa. This transfer of metal ions through the electric double layer (here assumed infinitely thin) takes place simultaneously in both directions. The amount of this transference is generally not equal in both directions and gives rise to the metal-electrolyte potential difference. This electrode potential is the potential difference that forms at the boundaries of the two phases. 

Electric Double Layer and Fractal Structure of Surface Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or non-faradaic) at a given applied potential. The main difficulty in the analysis of impedance spectra of solid electrodes is the frequency dispersion of the impedance values, referred to the constant phase or fractal behavior and modeled in the equivalent circuit by the so-called constant phase element (CPE) [5,15,16, 22, 35, 36]. The frequency dependence is usually attributed to the geometrical nonuniformity and the roughness of PC surfaces having fractal nature with so-called selfsimilarity or self-affinity of the structure resulting in an unusual fractal dimension... 

Under negative polarization of a nanotextured carbon electrode in aqueous electrolyte, hydrated cations are first adsorbed forming an electrical double layer. When the electrode potential is lower than the equilibrium value for water reduction, nascent hydrogen is formed (Eq. 12.7) and adsorbed onto the carbon surface [34] (Eq. 12.8) ... 

When a metal is in contact with an electrolyte solution, a dc potential occurs which is the result of two processes. These are (1) the passage of metallic ions into solution from the metal, and (2) the recombination of metal ions in the solution with free electrons in the metal to form metal atoms. After a metal electrode is introduced into an electrolyte, equilibrium is eventually established and a constant electrode potential is established (for constant environmental conditions). At equilibrium, a dipole layer of charge (electrical double layer) exists at the metal-electrolyte interface. There is a surface layer of charge near the metal electrode and a layer of charge of opposite sign associated with the surrounding solution. Although diffuse, this dipole layer produces an effective electrical capacitance (Cp) which accounts for the low-frequency behavior of the electrode polarization impedance as discussed in Chapters 2, 3, and 4. 

Electrical neutrality is established near the surfaces of the particles and a charge with the opposite sign, equivalent to the surface charge, gathers like a cloud in the form of ions around the particle surface (refer to Figure 54). In this structure, the layer attached to the particle surface is called the Stem layer, and outside that, the layer that is present as a result of equilibrium distribution through the balance between electrostatic attraction and diffusion force from thermal motion, is called the diffuse electric double layer. If an external electric field is applied to this kind of dispersion system, the particle and diffuse electric double layer are drawn electrically to an electrode of the opposite sign, and relative motion occurs at the boundary of a certain slide plane . The potential of this slide plane is called the zeta potential, and it is used as the scale of surface potential [6, 7, 8]. 

The liberated electrons remain in the electrode and thus produce a negative, electric potential in relation to the surrounding electrolyte. At equilibrium, an electric double layer [e Zn++] is created over the boundary layer between elec-trode/electrolyte. The resulting potential difference over the boundary layer is an indication of the tendency of the zinc metal to dissolve. 

Figure 6.17. At the interface between a zinc electrode and a surrounding electrolyte, equilibrium Zn Zn + 2e is obtained as the zinc atoms have a certain tendency to dissolve into ions the liberated electrons remain in the zinc electrode. Due to electrostatic attraction between ions and electrons, an electric double layer over the interface is built up. The magnitude of the resulting potential difference is a measure of the oxidation tendency of the zinc.

Suppose now that using an external source we apply to the working electrode the constant potential E, more negative than the equilibrium potential EJp). In this case the process that proceeds first is the charging of the electric double layer. During this process the electrochemical overpotential is rj, and changes with time according to the law ... 

Thermodynamics furnishes us with the relationship between the equilibrium Galvani potential at an electrode and the activity in solution of those ions which are able to penetrate the phase boundary, and hence the electric double layer. The difference in standard chemical potentials... 

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